A212747 Number of (w,x,y,z) with all terms in {0,...,n} and 2w=floor((x+y+z)/2).

1, 4, 13, 32, 63, 108, 171, 256, 365, 500, 665, 864, 1099, 1372, 1687, 2048, 2457, 2916, 3429, 4000, 4631, 5324, 6083, 6912, 7813, 8788, 9841, 10976, 12195, 13500, 14895, 16384, 17969, 19652, 21437, 23328, 25327, 27436, 29659, 32000

Offset

0,2

Comments

For a guide to related sequences, see A211795.

Links

Table of n, a(n) for n=0..39.

Index entries for linear recurrences with constant coefficients, signature (4,-7,8,-7,4,-1).

Formula

a(n)=4*a(n-1)-7*a(n-2)+8*a(n-3)-7*a(n-4)+4*a(n-5)-a(n-6).

G.f.: (1 + 4*x^2 + x^4)/((1 - x)^4 * (1 + x^2)).

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[2 w == Floor[(x + y + z)/2], s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
Map[t[#] &, Range[0, 45]]   (* A212747 *)

Crossrefs

Cf. A211795.

Sequence in context: A272510 A036487 A184632 * A011936 A037235 A363256

Adjacent sequences: A212744 A212745 A212746 * A212748 A212749 A212750

Keyword

nonn,easy

Author

Clark Kimberling, May 28 2012

Status

approved